Finite‐element modeling of the anthropoid mandible: The effects of altered boundary conditions

Abstract

Finite-element modeling provides a full-field method for describing the stress environment of the skull. The utility of finite-element models, however, remains uncertain given our ignorance of whether such models validly portray states of stress and strain. For example, the effects of boundary conditions that are chosen to represent the mechanical environment in vivo are largely unknown. We conducted an in vitro strain gauge experiment on a fresh, fully dentate adult mandible of Macaca fascicularis to model a simplified loading regime by finite-element analysis for purposes of model validation. Under various conditions of material and structural complexity, we constructed dentate and edentulous models to measure the effects of changing boundary conditions (force orientation and nodal constraints) on strain values predicted at the gauge location. Our results offer a prospective assessment of the difficulties encountered when attempting to validate finite-element models from in vivo strain data. Small errors in the direction of load application produce significant changes in predicted strains. An isotropic model, although convenient, shows poor agreement with experimental strains, while a heterogeneous orthotropic model predicts strains that are more congruent with these data. Most significantly, we find that an edentulous model performs better than a dentate one in recreating the experimental strains. While this result is undoubtedly tied to our failure to model the periodontal ligament, we interpret the finding to mean that in the absence of occlusal loads, teeth within alveoli do not contribute significantly to the structural stiffness of the mandible. © 2005 Wiley-Liss, Inc. Key words: mandible; computed tomography; image reconstruction; finite-element methodFinite-element analysis (FEA) is the method of choice for theoretical analysis of the mechanical behavior of complex shapes in biology. The approach of FEA approximates real geometry using a large number of smaller simple geometric elements (e.g., triangles, bricks, tetrahedrons). Since complex shapes defy simple mathematical solution (i.e., in terms of engineering formulas), FEA simplifies a problem by analyzing multiple simple elements of known shapes with established mathematical solutions. These multiple solutions are in the end combined together to depict states of stress and strain through the entire structure.The last half of the 20th century saw increasing interest in testing and analysis of bone biomechanics (Cowin, 2001), including increased use of finite-element (FE) methods. Many theoretical and experimental studies have sought to quantify the distribution of stresses and strain in the mandible (Knoell, 1977;Hylander, 1984;Bouvier

Modeling the Human Mandible Under Masticatory Loads: Which Input Variables are Important?

“…Consequently, there is a need to assess the effects of changes in the orientation of muscle vectors on the FEA results. Again, previous work with a macaque mandible showed that changing the orientation of external forces has a significant effect on FEA results (Marinescu et al, 2005).…”

“…This result can be explained by the fact that the inclusion of PDL as compliant material effectively creates large holes in the mandibular corpus, which reduces the second moment of inertia of the corpus and lowers its neutral axis under bending (Marinescu et al, 2005;Daegling et al, 2008;Gr€ oning et al, 2011a). It is also likely that the polar moment of inertia is reduced so that resistance to torsion decreases.…”

“…In vitro loading experiments with human mandibles have shown that the mandible indeed behaves as an open section under bending, but as a closed section under torsion (Daegling et al, 2008). Conducting a validation study with a macaque mandible Marinescu et al (2005) found that an FE model in which teeth and bone were modeled as continuous was far too stiff, while an edentulous FE model predicted strains that were much closer to the measured values. We obtained similar results in a recent sensitivity analysis (Gr€ oning et al, 2011a), where an FE model of a human mandible in which teeth and bone were modeled as continuous showed much lower strains in the mandibular corpus than a model with PDL.…”

“…In addition, the effects of different degrees of freedom at the constrained nodes need to be assessed. Marinescu et al (2005) observed large effects on strains in their FE model of a macaque mandible.…”

“…The relative importance of these modeling decisions on the results of an FEA can be estimated by sensitivity analyses (e.g., Dar et al, 2002;Marinescu et al, 2005;Ross et al, 2005;Bright and Rayfield, 2011;Gr€ oning et al, 2011a). During a sensitivity study, one or more model properties are varied and the effects on the calculated stresses and strains are quantified.…”